L. Antoine
constructed
a Cantor set in \(\mathbb {R}^2\) 
whose projections coincide
with those of a regular hexagon
[1]}.
Other examples
of Cantor sets in plane
all of whose projections are segments can be found in
[2]},
[3]}.
Using Antoine's idea, we
show that in \(\mathbb {R}^2\) ,
each polygon contains a Cantor set
with exactly the same projections (Statement REF ).
